TY - JOUR

T1 - On the streamline upwind scheme of solution to the filtration problem

AU - Ivanov, Maxim I.

AU - Kremer, Igor A.

AU - Laevsky, Yuri M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The work is devoted to one of the approaches in the numerical simulation of filtration processes of a two-phase incompressible fluid. Bukley - Leverett problem is considered with solutions of a shock wave type. Within the mixed finite element method upwind algorithm for solution to equation for saturation is proposed, which gives solutions without numerical oscillations at the discontinuity. Special attention is paid to a new approach to solving the degenerate Neumann problem in a mixed formulation for the pressure and total flow velocity. The work is accompanied by an illustration of the results of numerical experiments for 3D problem.

AB - The work is devoted to one of the approaches in the numerical simulation of filtration processes of a two-phase incompressible fluid. Bukley - Leverett problem is considered with solutions of a shock wave type. Within the mixed finite element method upwind algorithm for solution to equation for saturation is proposed, which gives solutions without numerical oscillations at the discontinuity. Special attention is paid to a new approach to solving the degenerate Neumann problem in a mixed formulation for the pressure and total flow velocity. The work is accompanied by an illustration of the results of numerical experiments for 3D problem.

KW - Filtration

KW - Immiscible fluid flow

KW - Injection well

KW - Mixed finite element method

KW - Production well

KW - Two-phase fluid

KW - Upwind scheme

UR - http://www.scopus.com/inward/record.url?scp=85071188574&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=42735095

U2 - 10.33048/semi.2019.16.051

DO - 10.33048/semi.2019.16.051

M3 - Article

AN - SCOPUS:85071188574

VL - 16

SP - 757

EP - 776

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -